Rust also has the complication that function pointers are not guaranteed to have an unique identity; If multiple functions compile to the same code, the compiler is allowed de-duplicate them.
The documentation [0] also warns it's also possible for the compiler to create multiple versions of the same function. And while I've absolutely seen the compiler to create multiple optimised versions of functions in disassembled code (partial inlining based on the caller), I'm not sure it's possible to get pointers to more than one version.
C++ actually did end up evolving the ability to define a zero-sized class without a unique memory address, but mostly to allow optimizations like the empty base optimization to apply in other situations where it could make sense, especially with templated or constexpr code.
Did it? Are you talking about the no_unique_address attribute (I had to go look that up because WG21 apparently doesn't care about consistently using or not using separators in attribute names) ? That attribute lets you do the same trick as empty base class but without the ceremony, however it doesn't let you make ZSTs.